Integrating Flood Depth, Duration, and Structural Damage in Vulnerability Surface Modelling Using Empirical Regression

Abstract Flood vulnerability assessment is critical for enhancing disaster risk reduction in regions exposed to compound flooding. This study presents a novel approach by developing flood vulnerability surfaces through the integration of flood depth, flood duration, and damage ratio across various housing typologies using a polynomial regression model. Unlike conventional models that primarily rely on flood depth, this study incorporates flood duration to better capture the non-linear and synergistic effects of prolonged inundation on structural damage. Three housing typologies, i.e., Non-Permanent, Semi-Permanent, and Permanent were analyzed, each with sub-types reflecting variations in construction material and resilience. Using empirical field survey data from a flood-prone district, three-dimensional (3D) surface models were constructed. Polynomial regression demonstrated superior performance, with coefficients of determination (R²) ranging from 0.92 to 0.97 across typologies. Notably, the Non-Permanent Type D structure reached a damage ratio of 0.9 at a flood depth of 2.5 m and a duration of 10 days, indicating extreme vulnerability. Semi-permanent structures such as Type B and C experienced damage ratios of 0.8–0.9 under flood depths of 3–4 m and durations exceeding 12 days. In contrast, Permanent structures showed more resistance, with damage ratios remaining below 0.6 under similar conditions, but rising rapidly above 0.85 when exposed to depths greater than 4 m and durations over 12 days. These 3D vulnerability surfaces provide clear visualizations of how flood parameters influence structural damage, improving the interpretability of risk assessments. The findings highlight the importance of typology-specific modelling to address local structural differences. This study offers a robust and flexible method for accurately modelling flood vulnerability, supporting the design of targeted mitigation measures and resilient housing strategies tailored to varying structural capacities under compound flood hazards.